In this talk we will discuss the infinite population limit of non-Markovian, finite-player stochastic differential games. Examples of such games include optimal execution in non-Markovian models or games with delay. We will argue that the weak formulation of the game is particularly well-suited for their analysis in the present non-Markovian setting. The asymptotics of the finite population game will be discussed based on a new form of propagation of chaos involving interacting particles with interactions through the control process of a system of backward stochastic differential equation. Finally, some seemingly new existence results will be discussed. This is based on a joint work with Dylan Possamaï.